EXCHANGE 


Wave  Lengths  of  the  Tungsten 
X-Ray  Spectrum 


A  DISSERTATION 


SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  COLLEGE   OF  THE 

STATE    UNIVERSITY   OF   IOWA     IN    PARTIAL    FULFILLMENT 

OF  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF   DOCTOR  OF  PHILOSOPHY 


By 

ELMER  DERSHEM 
1917 


Wave  Lengths  of  the  Tungsten 
X-Ray  Spectrum 


A  DISSERTATION 


SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  COLLEGE   OF  THE 

STATE    UNIVERSITY   OF   IOWA     IN    PARTIAL    FULFILLMENT 

OF  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF   DOCTOR  OF  PHILOSOPHY 


By 

ELMER  DERSHEM 
1917 


Reprinted  from  the  PHYSICAL  REVIEW,  N.S..  Vol.  XI,  No.  6,  June,  1918. 


WAVE-LENGTHS   OF  THE  TUNGSTEN   X-RAY    SPECTRUM. 

BY  ELMER  DERSHEM. 

INTRODUCTION. 

OINCE  the  X-ray  spectra  of  practically  all  the  available  elements 
^  had  been  studied  by  one  investigator  or  another  with  results  which 
did  not  very  closely  agree  and  which  in  general  comprised  only  a  few  of 
the  principal  or  most  prominent  lines,  it  seemed  wise  to  begin  the  present 
investigation  with  a  view  to  determining  more  completely  and  accurately 
than  heretofore  the  number  of  lines  and  their  wave-lengths  in  the  spec- 
trum of  at  least  one  element.  The  element  most  easily  tested  and  the 
one  whose  spectrum  would  be  of  the  greatest  value  in  the  X-ray  analysis 
of  crystals  was  tungsten  on  account  of  its  use  as  the  anticathode  of  the 
Coolidge  tube,  the  only  type  of  tube  which  could  be  used  during  the  long 
intervals  of  time  necessary  to  secure  spectral  photographs,  if  the  condi- 
tions required  for  the  greatest  resolving  power  and  the  greatest  accuracy 
of  measurement  were  complied  with. 

The  photographic  method  was  chosen  for  this  work  in  preference  to  an 
ionization  chamber  and  electrometer  because  in  the  latter  method  the 
intensity  of  the  reflected  beam  must  be  great  enough  to  give  a  continuous 
effect  on  the  electrometer  while  the  photographic  plate  gives  a  summation 
of  the  intensity  of  the  reflected  beam  over  a  time  that  may  be  made  so 
very  much  longer  that  weak  lines  have  an  opportunity  to  appear. 

We  shall  now  consider  the  factors  affecting  the  accuracy  of  measure- 
ment and  resolving  power  of  an  instrument  using  a  crystal  as  a  diffraction 
grating  for  X-rays.  Resolving  power  is,  as  usual,  defined  as  the  ratio 
of  a  wave-length  to  the  smallest  difference  which  may  exist  between  this 
and  a  neighboring  wave-length  and  yet  have  the  instrument  show  that 
the  two  waves  are  separate  and  not  identical.  A  consideration  of  these 
factors  will  then  show  that  the  conditions  for  the  best  resolving  power 
are  those  which  lead  to  a  decrease  in  intensity  and  would  make  impossible 
the  securing  of  sufficient  intensity  to  affect  an  electrometer  under  the 
necessary  conditions  of  a  narrow  source,  great  distance  from  the  crystal 
to  the  detector  and  a  thin  crystal  which  means  less  intensity  because 
there  are  fewer  reflecting  planes.  The  theory  will  also  show  that  the 
position  of  the  central  maximum  of  the  reflected  beam  is  not  the  true 
criterion  by  which  the  wave-length  must  be  determined  but  it  is  instead 


465867 


462  ELMER   DERSHEM. 

the  outer  edge,  which  when  corrections  are  made  for  the  width  of  the 
source,  gives  the  true  measurement.  The  impossibility  of  measuring 
anything  other  than  the  central  maximum  with  an  ionization  chamber 
eliminates  this  as  a  possible  accurate  method  and  leaves  the  photographic 
plate  as  the  only  recourse. 

RESOLVING  POWER  OF  A  CRYSTAL  USED  AS  A  DIFFRACTION  GRATING 

FOR  X-RAYS. 

In  this  discussion  the  assumption  will  be  made  that  the  slit,  or  source, 
is  the  same  distance  from  the  crystal  as  is  the  photographic  plate.  In 
this  case,  as  shown  by  Bragg,1  the  amount  of  surface  of  the  crystal 
exposed  to  the  X-rays  makes  no  difference  in  the  sharpness  of  the  lines 
since  the  same  wave-length  is  always  reflected  to  the  same  point  on  the 
plate.  This  will  not  be  true  if  the  atomic  planes  are  not  parallel.  In 
reality  the  cleavage  surfaces  of  crystals  are  quite  noticeably  warped 
and  it  is  desirable  to  limit  the  surface  of  the  crystal  exposed  to  the  rays 
by  means  of  a  narrow  slit  between  lead  blocks  placed  close  to  the  crystal 
even  though  it  does  cause  a  decrease  in  intensity.  It  will  also  be  assumed 
that  the  crystal  is  thin  enough  that  the  rays  may  penetrate  entirely 
through  the  crystal  and  be  reflected  from  the  planes  on  the  back  side 
and  again  traversing  the  crystal  to  reach  the  photographic  plate. 

With  these  assumptions  as  to  con- 
ditions which  may  be  easily  obtained 
in  practice,  the  question  to  be  deter- 
mined is,  What  difference  of  wave- 
length is  necessary  that  it  may  be 
possible  to  separate  two  waves  of 
nearly  the  same  length? 
Let  the  source  be  a  slit  of  width  s  at  a  distance  r  from  the  crystal, 
Fig.  I.  Assume  that  the  crystal  is  in  a  position  to  reflect  some  particular 
wave-length  where  n\  =  2d  sin  0,  in  which  n  is  the  order  of  the  spectrum, 
X  the  wave-length,  d  the  grating  constant  or  distance  between  the 
atomic  planes  and  0  the  angle  between  the  incident  rays  and  the  crystal 
surface.  Then  a  ray  coming  from  the  side  M  of  the  slit  may  be  reflected 
at  A  to  A '  on  the  photographic  plate  and  a  ray  from  the  side -TV  must 
strike  the  crystal  at  the  same  angle  and  consequently  be  reflected  at  the 
point  B  to  the  point  B'.  It  is  easily  seen  that  the  reflected  rays  A  A' 
and  BB'  are  at  the  same  distance  apart  as  the  incident  rays  MA  and 
NB.  Hence  due  to  the  slit  alone  a  single  wave-length  would  cause  a 
line  on  the  photographic  plate  the  same  width  as  the  slit. 

1  Bragg  and  Bragg,  X-Rays  and  Crystal  Structure,  G.  Bell  and  Sons,  London,  1915. 


TUNGSTEN   X-RAY   SPECTRUM.  463 

Considering  next  the  question  of  the  variation  of  the  width  of  image 
with  the  thickness  of  the  crystal,  let  DE  be  drawn  perpendicular  to  A  A'. 
Then  DE  is  the  width  of  the  reflected  beam  due  to  the  penetration  into 
the  crystal.  Let  DF  =  t  be  the  thickness  of  the  crystal.  Then 
/  =  AD  sin  B  and 

DE 

^  =  sin  20- 
Then  by  substitution 

DE  sin  B         DE  sin  9  DE 


t 


sin  20       "  2  sin  0  cos  0      2  cos  0 


Whence  DE  =  2t  cos  0. 

Since  DE  is  the  width  of  beam  due  to  penetration  into  the  crystal  the 
total  width  of  beam  is  5  +  2t  cos  6,  in  which  5  is  the  width  of  the  slit, 
or  source,  t  the  thickness  of  the  crystal  and  B  the  angle  which  the  incident 
ray  makes  with  the  crystal. 

Then  s  +  2t  cos  6  is  the  width  of  the  line  on  the  photographic  plate. 
In  order  to  resolve  two  lines  of  nearly  the  same  wave-length  it  is  necessary 
that  their  images  on  the  plate  should  not  overlap  or,  in  other  words, 
that  the  centers  of  their  images  must  be  further  apart  than  the  width 
of  beam,  s  -\-  2t  cos  B. 

Assume  two  wave-lengths,  X  and  X  +  AX.  To  find  how  small  AX 
may  be  and  these  wave-lengths  still  be  clearly  resolved  on  the  plate. 
Using  the  formula  n\  =  2d  sin  B  let  X  take  on  a  small  increment  AX 
and  B  the  corresponding  increment  A0. 
Then  by  differentiation  we  have  wAX 
=  2d  cos  0A0.  This  is  justified  in 
practice  by  the  fact  that  A0  is  small 
in  comparison  to  0. 

According  to  the  above  if  the  crys-      D«u«^  ^  Cryet4l 

tal  is  in  a  position  to  reflect  a  wave 

rig.  2. 

of  length  X  it  must  rotate  through  an 

angle  A0  in  order  to  reflect  a  wave  of  length  X  +  AX  and  since  the  re- 
flected ray  rotates  twice  as  fast  as  the  crystal  the  reflected  ray  must 
rotate  through  the  angle  2A0.  (See  Fig.  2.) 

If  the  distance  of  the  crystal  from  the  plate  is  r  then  the  displacement  of 
the  beam  along  the  plate  when  the  reflecting  angle  is  changed  from  0  to 
0  +  A0  is  2rA0.  In  order  that  rays  reflected  at  these  angles  be  separated 
it  is  necessary  that  this  distance,  2rA0  be  greater  than  the  width  of  beam 

S  +  2t  COS  0. 

2rA0  >  5  +  2/  cos  0. 
But 


464  ELMER   DERSHEM. 

WAX 

A0  =  -r- 

2d  cos  6 

and  by  substitution 

O^Y\\ 

>  S  +  2t  COS  0 


2d  COS  0 

d  cos  6  . 
AX  > (s  +  2/  cos  (9). 

AX  is  then  the  smallest  difference  between  the  lengths  of  two  waves 
that  is  permissible  if  the  images  due  to  these  waves  are  to  be  separated 
on  the  plate.  However  the  images  must  be  separated  by  a  slightly 
greater  distance  in  order  to  leave  a  clear  space  between  them.  Just  how 
much  space  is  necessary  for  this  is  not  a  mathematical  problem  but  a 
question  which  must  be  answered  by  experience.  Probably  but  little 
need  be  added  to  AX  on  this  account.  Neglecting  for  the  time  being  the 
question  of  the  necessary  space  between  lines  it  may  be  of  interest  to 
determine  the  resolving  power  under  the  best  conditions  that  were 
obtained  with  the  apparatus  used  in  the  present  work.  For  example, 
taking  the  line  in  the  central  part  of  the  L  spectrum  having  a  wave- 
length of  1.241  X  io~8  cm.  the  experimental  values  of  the  quantities 
contained  in  the  above  formula  were : 

^  =  0.032  cm., 
/  =  0.019  cm., 
d  =  2.814  X  io~8  cm., 
r  =  62  cm., 
cos  0  =  0.977, 

n  =  I. 
Substituting  in  the  inequality 

d  cos  6  . 

(S  +  2t  COS  ff) 

the  above  values  of  the  quantities  gives 

AX  >  0.00375  X  io~8  cm. 

Since  resolving  power  is  defined  as  X/AX  and  for  this  case  X  is 
1.241  X  io~8  cm.  we  have 

A  <  I'24I 
AX  *  .00375  ' 

X 


1']  TUNGSTEN  X-RAY  SPECTRUM.  465 

The  resolving  power  in  this  case  was  less  than  331,  although  the  experi- 
mental values  of  the  width  of  slit,  thickness  of  crystal  and  distance  to 
the  plate  were  so  chosen  as  to  give  the  greatest  possible  resolving  power 
consistent  with  the  necessary  requirement  of  retaining  sufficient  intensity 
in  the  reflected  beam  to  affect  the  photographic  plate  in  an  exposure  of 
a  reasonable  duration. 

It  is  apparent  that  the  ways  in  which  the  resolving  power  may  be 
increased  are  to  use  a  higher  order  than  the  first,  to  narrow  the  source, 
to  decrease  the  thickness  of  the  crystal  and  to  increase  the  distance 
between  the  crystal  and  the  plate.  To  do  any  one  of  these  things  tends 
to  decrease  the  intensity  and  make  necessary  a  longer  exposure  and  this 
is  not  altogether  desirable,  as  it  gives  the  latent  image  an  opportunity  to 
spread  and  blurr  the  image  and  also  increases  the  liability  to  fogging  of 
the  plate  due  to  stray  radiation.  An  increase  of  distance  from  crystal 
to  plate  decreases  the  intensity  by  absorption  in  the  air  and  this  may  be 
a  factor  of  considerable  importance  in  working  with  the  longer  wave- 
lengths. Therefore  at  present  it  would  not  seem  possible  to  so  greatly 
increase  the  resolving  power  of  a  crystal  used  as  a  diffraction  grating  for 
X-rays  as  to  make  it  at  all  comparable  to  the  resolving  powers  of  the 
grating  or  echelon  used  for  ordinary  light. 

From  this  theory  it  may  be  seen,  by  reference  to  Fig.  I,  that  the  true 
angle  of  reflection  must  be  determined  by  measuring  the  position  of  the 
outer  edge  or  most  deviated  portion  of  the  spectral  line  and  subtracting 
one  half  of  the  width  of  the  source  from  this.  This  will  eliminate  any 
error  of  measurement  due  to  penetration  into  the  crystal  but  the  crystal 
must  be  thin  if  two  nearly  equal  wave-lengths  are  to  be  separated. 

METHODS  OF  APPLYING  THE  THEORIES  CONCERNING  RESOLVING  POWER. 

Since  it  was  the  object  in  this  work  to  make  as  accurate  measurements 
of  the  wave-lengths  as  possible  the  apparatus  and  methods  of  using  it 
will  be  described  somewhat  in  detail. 

The  previous  theory  requiring  the  use  of  a  thin  crystal,  the  following 
method  of  securing  and  mounting  one  was  adopted.  A  crystal  of  rock 
salt  having  a  perfect  cleavage  face  of  about  one  square  centimeter  area 
was  chosen  and  this  was  fastened  face  down  onto  a  glass  surface  by  the 
use  of  a  wax  especially  prepared  for  the  purpose  by  mixing  Canada 
balsam  and  hard  sealing  wax  in  such  proportions  as  would  give  a  wax 
that  was  hard  and  tough  at  ordinary  temperatures  but  which  became  a 
thin  liquid  when  slightly  heated.  After  the  crystal  was  firmly  cemented 
to  the  glass  by  pressing  the  two  together  while  warm  with  a  small  quantity 
of  wax  between  and  allowing  them  to  cool,  the  crystal  was  ground  away 


466  ELMER   DERSHEM. 

until  a  thickness  of  not  more  than  0.019  cm-  remained.  It  was  found  by 
experience  that  attempts  to  make  the  crystal  thinner  than  this  resulted 
in  causing  the  crystal  to  crack  and  become  useless. 

The  measurements  of  the  position  of  the  lines  on  the  photographic 
plates  were  made  with  a  Societa  Genevoise  dividing  engine  which  was 
guaranteed  by  the  makers  to  be  accurate  to  o.oi  mm.  in  a  total  length 
of  40  cm. 

To  check  against  possible  variations  in  the  pitch  of  the  screw  the  plates 
were  measured  a  number  of  times  and  each  time  the  setting  was  changed 
so  that  the  measurement  would  be  made  by  a  different  part  of  the  screw. 
However  the  principal  object  of  repeating  the  measurements  was  to 
compensate  for  the  errors  of  setting  by  securing  a  number  of  readings 
and  averaging  the  results. 

A  number  of  different  methods  of  securing  accurate  settings  of  the 
dividing  engine  were  tried  and  the  one  giving  the  most  consistent  results 
was  the  following.  An  achromatic  combination  lens  of  if  inches  diameter 
was  placed  in  a  tube  22  inches  long.  Two  parallel  hairs  were  placed  at 
one  end  of  the  tube  and  brought  very  close  to  the  photographic  plate 
so  that  the  parallel  hairs  and  the  spectral  line  on  the  plate  should  be 
practically  in  one  conjugate  focal  plane  of  the  instrument  at  the  same 
time.  The  spectral  line  and  the  parallel  hairs  were  then  viewed  through 
a  peep  hole  at  the  other  end  of  the  tube  which  was  near  the  other  con- 
jugate focus  of  the  lens.  Owing  to  the  great  length  of  the  tube  as  com- 
pared to  the  distance  between  the  parallel  hairs  and  the  photographic 
plate  there  was  very  little  parallax  and  owing  to  the  large  diameter  of  the 
lens  the  field  of  view  was  large  enough  to  avoid  to  a  considerable  extent 
the  loss  of  contrast  .that  comes  from  magnifying  a  small  section  of  surface 
which  shades  gradually  from  one  portion  to  another.  It  is  this  difficulty 
that  makes  it  impossible  to  use  the  ordinary  microscope  having  a  small 
objective.  To  secure  proper  illumination  the  apparatus  was  placed  so 
that  the  observer  looked  through  the  plate  toward  a  clear  sky. 

Whenever  two  objects  are  very  close  together  they  appear  to  blend 
into  one,  especially  if  the  edges  are  not  sharp  and  clearly  defined.  Owing 
to  this  effect  as  the  photographic  line  approaches  the  parallel  hairs  of  the 
microscope  it  blends  with  them  while  not  really  coinciding  with  them. 
To  avoid  as  far  as  possible,  the  inaccuracies  due  to  this  effect,  small  dots 
were  made  with  the  point  of  a  needle  as  nearly  as  possible  along  the 
outer  edge  of  the  line  and  it  was  then  possible  while  the  line  was  in  the 
field  of  view  of  the  microscope  and  yet  not  too  close  to  the  parallel  hairs 
to  choose  the  particular  dot  which  most  nearly  denoted  the  position 
of  the  edge  of  the  line  and  then  take  the  measurement  when  this  dot 
came  exactly  between  the  parallel  hairs. 


NoL6XI]  TUNGSTEN  X-RAY  SPECTRUM.  467 

DESCRIPTION  OF  APPARATUS  USED  IN  SECURING  THE  X-RAY  SPECTRUM. 

The  apparatus  used  in  this  work  can  perhaps  best  be  described  by 
referring  to  the  isometric  drawing  of  the  framework,  Fig.  3. 

The  mechanism  was  enclosed  in  a  box  lined  with  sheet  lead  J  inch 
thick  in  order  to  cut  out  stray  radiation,  but  for  simplicity  this  is  not 
shown  in  the  drawing.  The  crys- 
tal was  mounted  on  the  rotating 
axis  A  which  was  fitted  with  ad- 
justable bearings  such  that  this 
axis  could  be  made  truly  vertical 
with  respect  to  the  horizontal 
plane  of  the  instrument.  Between 
the  source  and  the  crystal,  as 
close  as  possible  to  the  latter,  a  F- 

vertical  lead  plate  f    inch   thick 

was  placed.  This  is  not  shown  in  the  drawing.  The  area  of  crystal 
surface  upon  which  the  X-rays  might  strike  was  limited  by  a  slot  3 
mm.  wide  cut  through  the  center  of  this  plate. 

One  end  of  the  framework  of  cast  iron  and  steel  carried  the  block  of 
lead  L  which  was  about  2  inches  thick  and  of  sufficient  area  to  subtend 
a  solid  angle  at  the  anticathode  of  the  X-ray  tube  greater  than  that 
subtended  by  the  photographic  plate  and  in  this  way  served  to  protect 
the  plate  from  the  direct  radiation  of  the  tube.  The  previously  men- 
tioned lead-lined  box  enclosing  the  apparatus  served  to  protect  the  plate 
from  the  radiation  reflected  from  the  walls  of  the  room.  A  slot  about 
3/16  inches  wide  was  cut  through  the  center  of  this  block  of  lead  and  this 
slot  was  covered  by  the  two  lead  plates  or  jaws  P  and  Pf  which  had  their 
inner  surfaces  plane  polished  and  which  could  be  set  at  any  distance 
apart  by  means  of  gauges  placed  between  their  upper  and  lower  edges. 
The  slot  or  space  between  these  two  surfaces  could  then  be  considered 
as  the  source  of  the  X-rays,  since  it  was  sufficiently  close  to  the  focal 
spot  of  the  target  that  this  spot  subtended  a  larger  angle  at  the  slit  than 
did  the  crystal,  the  latter  being  comparatively  far  away. 

The  other  end  of  the  framework  carried  a  bar  of  angle  steel,  the  vertical 
surface  5  of  which  was  planed  true  and  then  set  accurately  at  right  angles 
to  the  line  joining  the  center  of  the  source  and  the  center  of  the  rotating 
axis  on  which  the  crystal  was  mounted.  The  photographic  plate  was 
placed  in  a  light-proof  envelope  and  clamped  tightly  to  this  surface  and 
since  the  distance  of  the  surface  from  the  center  of  rotation  of  the 
crystal  could  be  accurately  determined  by  means  of  a  bar  of  adjustable 
length  which  could  later  be  measured  on  the  dividing  engine,  it  was 


468  ELMER   DERSHEM.  [ 


SECOND 
SERIES. 


possible  to  determine  the  distance  of  the  film  from  the  center  of  rotation 
by  subtracting  the  thickness  of  the  plate  and  the  paper  back  of  the  plate 
from  the  measured  length  of  the  bar. 

The  mechanism  for  holding  the  crystal  is  shown  in  Fig.  4.  One  side 
of  the  shaft  A  was  plane  surfaced  as  was  also  the  block  of  brass  F  and 
these  could  be  firmly  clamped  together  by  the  two  screws  H  and  K. 
These  surfaces  could  then  be  separated  and  placed  together  at  will, 
always  fitting  together  in  the  same  position.  The 
block  F  carried  the  block  E  attached  to  it  by  three 
screws  in  such  a  way  that  the  surface  BC  could  be 
adjusted  to  the  desired  plane  and  then  locked 
there  by  the  pressure  of  the  screw  I.  With  the 
shaft  set  in  its  bearings  the  upper  and  lower  parts 
of  the  surface  BC  were  adjusted  until  when  viewed 
through  a  microscope  both  the  upper  and  lower 
edges  remained  in  the  axis  of  rotation  as  the  shaft 

_  was  rotated.     Then  this  surface  BC  would  contain 

Fig.  4. 

the  axis  of  rotation  and  by  pressing  a  crystal 

surface  against  this' face  plate  and  waxing  firmly  from  behind,  the  crys- 
tal surface  would  also  contain  the  axis  of  rotation.  The  face  plate 
could  then  be  removed  by  taking  out  the  screws  H  and  K  and  the 
crystal  would  be  left  properly  mounted. 

The  axis  A  was  made  perpendicular  to  the  framework  by  first  placing 
a  piece  of  silvered  glass  in  the  position  of  the  crystal  and  adjusting  the 
bearings  until  the  image  of  a  straight  horizontal  line  drawn  along  the 
middle  of  the  surface  S  was  projected  back  onto  the  line  at  all  points 
as  the  axis  was  rotated.  When  these  adjustments  were  made  it  was 
assured  that  the  axis  of  the  shaft  bearing  the  crystal  was  perpendicular 
to  the  horizontal  plane  of  the  instrument  and  that  whenever  a  crystal 
face  was  placed  against  the  removable  face  plate  its  surface  would  also 
contain  the  axis  of  rotation.  The  only  other  adjustment  was  to  set  the 
apparatus  as  a  whole  so  that  the  slot  between  the  jaws  P  and  Pr  was  on 
the  straight  line  joining  the  focal  spot  and  the  axis  of  rotation  of  the 
crystal. 

It  was  necessary  to  have  a  precise  reference  line  marked  on  the  photo- 
graphic plate  near  the  point  where  the  undeviated  portion  of  the  X-ray 
beam  would  strike  in  order  that  a  photograph  might  be  taken  with  the 
crystal  set  to  reflect  toward  one  side  of  the  apparatus  and  later  one  taken 
on  another  plate  with  the  crystal  turned  to  reflect  to  the  other  side  of  the 
center  line.  From  these  two  plates  the  mean  distance  of  any  particular 
spectral  line  from  this  reference  line  could  be  found  and  having  once 


Na'6XL]  TUNGSTEN  X-RAY  SPECTRUM.  469 

determined  the  position  of  this  reference  line  with  respect  to  the  true 
center  it  was  possible  to  determine  the  true  deviation  of  any  wave-length 
from  a  photograph  taken  on  one  side  of  the  instrument.  To  check 
against  changes  of  position  the  instrument  was  frequently  calibrated  by 
taking  photographs  on  both  sides  of  the  center.  The  reference  line  was 
made  by  allowing  part  of  the  portion  of  the  X-ray  beam  which  passed 
undeviated  through  the  crystal  to  pass  through  the  narrow  slot  between 
the  two  plane  surfaced  lead  bars  N  and  N'  which  were  soldered  to  the 
brass  bars  M  and  M'  for  the  purpose  of  strength  and  stiffness.  These 
lead  surfaces  were  separated  by  thin  strips  of  paper  between  their  upper 
and  lower  edges  and  the  narrow  beam  of  X-rays  that  passed  through 
marked  a  very  fine  line  on  the  plate. 

While  the  photographs  were  being  taken  the  crystal  was  slowly 
rotated  by  means  of  a  fine  wire  which  extended  from  the  pulley  R, 
Fig.  3,  to  a  lever  which  was  connected  to  a  float  in  a  tank  of  water. 
Water  was  siphoned  into  this  tank  from  another  tank  in  which  the  level 
was  maintained  constant  and  by  regulating  the  rate  of  flow,  the  rate  of 
rising  of  the  float,  and  the  rotation  of  the  crystal  could  be  regulated  to 
any  value  desired. 

While  taking  the  photographs  of  the  L  radiation  the  current  for  the 
Coolidge  tube  was  supplied  by  a  transformer  excited  directly  from  the 
I  lO-volt  alternating  current  mains.  The  transformer  stepped  the  voltage 
up  to  a  maximum  potential  of  58,000  volts  and  the  tube  rectified  its  own 
current,  a  well-known  property  of  the  Coolidge  tube  provided,  as  in  this 
case,  that  the  temperature  does  not  become  too  high. 

In  order  to  avoid  the  necessity  of  remaining  in  the  room  during  the 
long  time  required  for  taking  the  spectral  photographs  a  motor-operated 
rheostat  was  placed  in  the  heating  circuit  of  the  Coolidge  tube  and  the 
motor  controls  were  placed  in  another  room.  A  wattmeter  in  this  room 
indicated  the  power  input  to  the  transformer  and  it  was  possible  by 
regulating  the  heating  current  of  the  tube  to  secure  any  power  input 
desired.  It  was  found  that  when  the  heating  current  was  such  that 
the  power  input  of  the  transformer  was  240  watts  the  target  remained 
at  a  cherry  red  heat  but  did  not  get  hot  enough  to  cause  damage  to  the 
tube.  Of  this  power  about  100  watts  went  to  supply  the  losses  in  the 
transformer  and  the  remaining  140  watts  represented  the  power  actually 
used  in  the  tube. 

For  the  K  radiations  the  same  method  was  followed  except  that  the 
applied  maximum  potential  was  raised  to  80,000  volts  and  the  current 
through  the  heating  circuit  was  set  at  such  a  value  as  to  cause  the  tube 
to  take  140  watts  from  the  transformer  as  before. 


47°  ELMER   DERSHEM. 

It  was  found  that  the  power  input  would  remain  constant  for  an  hour 
to  within  five  or  ten  watts,  hence  it  was  possible  to  work  at  other  things 
during  the  long  time  of  exposure  required  and  thus  the  labor  was  very 
much  reduced. 

EXPERIMENTAL  RESULTS  FOR  THE  L  RADIATIONS. 

Some  writers  on  this  subject  have  used  the  first  letters  of  the  alphabet 
to  designate  the  shorter  wave-lengths  and  others  have  used  these  same 
letters  to  indicate  the  longer  wave-lengths,  while  others  have  used  Greek 
letters.  Owing  to  these  confusing  methods  of  nomenclature  it  has  been 
thought  wise  to  submit  the  following  means  of  identifying  each  particular 
wave-length.  The  first  three  significant  figures  denoting  the  wave- 
length in  Angstrom  units  are  used  as  subscripts  to  the  Greek  letter  X 
which  is  usually  used  to  denote  a  wave-length.  If  the  knowledge  of 
X-ray  spectra  shall  increase  to  that  point  where  three  figures  no  longer 
distinguish  two  neighboring  wave-lengths  it  will  be  possible  to  use  four 
or  more  figures. 

In  the  experimental  work  a  number  of  photographs  were  taken  using 
different  distances  from  the  crystal  to  the  plate,  always  keeping  the 
distance  from  the  source  to  the  crystal  as  nearly  as  possible  equal  to  this 
distance.  The  method  of  procedure  is  shown  by  the  following  example. 
Plate  No.  104  was  placed  so  as  to  register  the  center  line  and  the  spectrum 
on  the  left  side.  Later  Plate  No.  105  was  similarly  placed  on  the  right 
side,  each  being  given  an  exposure  of  more  than  twenty-four  hours. 
When  measured^on  the  dividing  engine  the  distance  of  the  most  deviated 
side  of  the  spectral  line  Xi-2?  from  the  central  reference  line  was  found  to 
be  29.993  cm.  to  the  left  on  Plate  No.  104  and  3O.O39  cm.  to  the  right  on 
Plate  No.  105.  The  reference  line  was  therefore  one  half  of  the  difference 
or  0.023  cm.  to  the  left  of  the  true  center.  This  correction  could  then 
readily  be  applied  to  photographs  taken  later  on  only  one  side  of  the 
apparatus.  The  deviation  of  the  outer  edge  of  this  spectral  line  was 
therefore  3O.OI6  cm.  and  since  the  slit  width  was  0.032  cm.  subtracting 
one  half  of  this'  according  to  the  previous  theory  gives  the  true  deviation 
of  the  line  to  be  30.00°  cm.  The  distance  from  the  axis  of  rotation  of  the 
crystal  to  the  plateholder  was  61.10°  cm.,  from  which  must  be  subtracted 
the  thickness  of  the  plate  0.260  cm.,  also  the  thickness  of  the  paper 
envelope  enclosing  it,  which  was  0.013  cm.,  giving  6o.827  cm.  as  the 
distance  from  the  film  side  of  the  plate  to  the  axis  of  rotation.  The 
quotient  of  the  distance  from  the  center  to  the  spectral  line  divided  by 
the  distance  from  crystal  to  film  gives  the  tangent  of  twice  the  glancing 
angle  of  reflection  and  denoting  this  angle  by  6  we  have 


VOL.  XI.l 
No.  6. 


TUNGSTEN  X-RAY   SPECTRUM. 


47  I 


Tan  26  = 


30.00° 


Whence   6  =  13°   7'   35' 


60.827 ' 
from  which    by   the  use  of  the 


n\  =  2d  sin  6,  in  which  n  is  unity  and 
We  find  X  to  be  I.2781  X  io~8  cm. 


formula 
has  the  value  2.814  X  io~8  cm. 


TABLE  I. 

Summary  of  Results  for  The  L  Radiations  Wave-Lengths  X  10~8  Cm. 


Line. 

Plates  104 
and  105. 

Plates  115 
and  117. 

Plate  121. 

Plate  132. 

Plate  123. 

Average. 

AI  43       .  . 

1.4820 

1.4836 

1.4828 

Xl.47  

1.4719 

1.4725 

1.4723 

1.4722 

Xl.41  

1.4163 

1.4163 

AI  29 

1.2979 

1.2968 

1.2976 

1.2983 

1.2977 

Xl  28  

1.2868 

1.2868 

AI  27  

1.2781 

1.2781 

1.2780 

1.2784 

1.2793 

1.2784 

Xl.25  

1.2589 

1.2580 

1.2588 

1.2593 

1.2598 

1.2586 

Xi.24  

1.2418 

1.2412 

1.2413 

1.2414 

1.2421 

1.2416 

Xl  22    •  • 

1.2205 

1.2199 

.2202 

Xj.20  

1.2102 

1.2094 

.2098 

AI  17        ... 

1.1773 

.1773 

Xl.12  

1.1297 

1.1286 

.1292 

Xi.09  

1.0948 

1.0951 

1.0948 

1.0955 

1.0963 

.0953 

Xl.07  

1.0705 

.0705 

Xi.06  

1.0645 

1.0649 

1.0643 

1.0645 

1.0656 

.0648 

Xl.05  

1.0587 

1.0586 

1.0581 

1.0587 

1.0593 

.0587 

Xl.04  

1.0427 

1.042' 

Xi.02  

1.0250 

1.0246 

1.0258 

1.0250 

1.0262 

1.025» 

'X.,1  

.9153 

.9153 

.9158 

.9165 

.9171 

.9159 

X.70  

.7058 

.7079 

.7068 

'X.48  

.4835 

.4838 

.4838 

.4828 

.4838 

.4833 

1  Wave-lengths  shorter  than  X  .91  are  selectively  absorbed  by  the  bromine  in  the  plate 
causing  a  dark  band  at  the  position  of  this  wave-length. 

2  The  silver  of  the  plate  selectively  absorbs  wave-lengths  shorter  than  X  .48  thus  causing 
a  dark  band  at  the  position  of  this  wave-length. 

In  a  similar  way  the  angles  of  reflection  and  the  wave-lengths  were 
determined  for  the  other  characteristic  L  rays  and  the  results  of  five 
separate  tests  are  recorded  in  Table  I.  These  results  were  computed 
from  an  average  of  eight  separate  measurements  of  each  plate.  The 
agreement  between  the  different  tests  is  a  fair  test  of  the  accuracy  of 
the  work  since  the  distances  to  be  measured  were  different  in  each  case. 
Table  II.  gives  a  summary  of  the  results  of  different  investigators  each 
of  whom  had  either  used  rock  salt  crystals  directly  or  had  compared  the 
gtating  constant  of  some  other  crystal  with  that  of  rock  salt  so  that  in 
every  case  the  results  are  based  on  the  value  of  2.814  X  io~8  cm.  for  the 


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PHYSICAL  REVIEW,  VOL.  XL,  SECOND  SERIES. 
Tune.  1918. 


PLATE  I. 
Face  page  472. 


Fig.  5. 

Showing  the  position  of  the  19  lines  of  the  L  group  and  also  the  boundaries  of  regions  of 
greater  blackening  of  the  plate  corresponding  to  wave-lengths  of  .9159  and  .4833  Angstrom 
units  which  are  due  to  selective  absorption  by  the  bromine  and  silver  of  the  plate  of  waves 
just  shorter  than  their  own  K  radiations,  (de  Broglie,  Comptes  Rendus,  Vol.  158,  p.  1493, 
and  Vol.  163,  p.  87;  Wagner,  Annalen  der  Physik,  Vol.  46,  p.  868.) 

Lines  X  .48  are  Ag  absorption  lines,  the  upper  one  being  first  order,  the  lower  one  second 
order.  Line  X  .91  is  Br  absorption  line. 


Fig.  6. 
ELMER   DERSHEM. 


VOL.  XI.l 
No.  6.     . 


TUNGSTEN   X-RAY  SPECTRUM. 


473 


distance  between  the  atomic  planes  in  halite.     Fig.  5  is  a  photograph 
showing  the  position  of  the  L  lines  of  the  tungsten  spectrum. 

Before  doing  the  preceding  work  it  was  thought  possible  that  the 
distance  between  planes  of  atoms  in  a  crystal  might  not  be  identical  for 
all  crystals  of  the  same  substance  but  might  vary  with  the  conditions  of 
growth  of  the  crystal.  To  test  this  some  preliminary  measurements 
were  made  using  crystals  of  halite  obtained  from  different  parts  of  the 
earth.  The  results  showed  that  to  within  the  limits  of  error  of  measure- 
ment there  was  no  variation  of  the  grating  constant. 

EXPERIMENTAL  RESULTS  FOR  THE  K  RADIATIONS. 

In  securing  the  photographs  of  the  K  radiations  the  same  methods 
were  followed  as  in  the  case  of  the  L  radiations  except  that  a  higher 
potential  was  required.  On  account  of  the  great  penetrability  of  these 
rays  the  use  of  a  thin  crystal  was  much  more  imperative.  Fig.  6  shows 
a  photograph  of  the  four  K  lines  of  tungsten.  Owing  to  the  use  of  a 
thin  crystal  these  lines  are  all  clearly  separated  in  the  first  order.  Other 
observers  using  a  thick  crystal  have  found  difficulty  in  separating  the 
two  lines  of  shortest  wave-length  in  the  first  order.  Table  III.  gives  the 
results  of  four  tests  for  the  wave-lengths  of  the  K  lines  of  tungsten  and 

TABLE  III. 

THE  K  RADIATIONS  OF  TUNGSTEN. 
Wave-Lengths  in  Angstrom  Units. 


Plate  58. 

Plate  icg. 

Plate  114. 

Plate  119. 

Weighted 
Average. 

X  21  

.2121 

.2126 

.2118 

.2126 

.212* 

Xzo 

.2075 

.2075 

2069 

2078 

2076 

X.18  

Xn  

.1833 
.1784 

.1818 
.1786 

.1831 
.1778 

.1837 
.1785 

.183* 
1784 

TABLE  IV. 

A  COMPARISON  OF  THE  RESULTS  OBTAINED  BY  DIFFERENT  INVESTIGATORS  OF  THE  K 

RADIATIONS  OF  TUNGSTEN. 
Wave-Lengths  in  Angstrom  Units. 


de  Broglie, 
Comptes  Rendus, 
April,  1916. 

Hull, 
G.  E.  Review, 
July,  1916. 

Ledoux-Lebard 
and  Dauvillier, 
Comptes  Rendus, 
December,  1916. 

Dershem. 

<*K  .2032 

f  .212 
"  i.208 

<*i  .2128 
«2  .2053 

X.21 

X.20 

.212* 
.207' 

&.1768 

ft    .185 

ft  .1826 

X.18 

.183* 

ft  .1768 

X.17 

.178* 

474  ELMER   DERSHEM. 

Table  IV.  gives  a  comparison  with  the  results  of  other  observers.  In 
Table  III.  in  finding  the  weighted  average  the  last  plate  is  assigned  a 
weight  of  three  and  the  others  a  weight  of  unity  since  they  were  not  so 
perfect  as  the  last.  In  these  tests  the  distance  from  crystal  to  plate 
varied  slightly  for  the  different  plates,  but  was  always  between  60  and 
6 1  centimeters. 

ACCURACY  OF  THE  MEASUREMENTS. 

Since  the  extreme  variation  from  the  mean  value  is  not  greater  than 
o.i  per  cent,  for  any  characteristic  line  of  the  L  group  the  probable  error 
is  less  than  this  amount.  In  the  same  way  the  probable  error  for  the  K 
lines  is  less  than  0.8  per  cent.  On  account  of  the  smaller  angles  these 
cannot  be  so  easily  measured  as  the  L  lines. 

There  is  very  little  possibility  that  the  lines  observed  may  in  part  be 
due  to  impurities  in  the  tungsten  target.  I  have  no  direct  information 
in  regard  to  the  purity  of  the  latter  but  understand  that  no  impurities 
can  be  shown  by  chemical  analysis. 

These  results  agree  well  with  such  results  as  are  reported  by  Siegbahn 
and  Friman  and  also  with  those  computed  from  the  values  of  the  reflec- 
tion angles  as  given  by  de  Broglie  but  disagree  with  most  of  the  others. 
This  is  to  be  expected  in  some  cases.  Gorton  used  a  film  wrapped  onto 
a  cylindrical  surface.  It  would  seem  possible  that  the  film  might  either 
shrink  or  stretch  in  the  process  of  development.  Compton  recorded  the 
deflections  of  an  electrometer  photographically  on  a  moving  film.  This 
gives  a  graphical  representation  of  the  relative  intensities  of  the  different 
lines  but  it  would  be  difficult  to  get  a  precise  measurement  of  wave-length 
in  this  way  since  the  angular  position  of  the  crystal  is  not  accurately 
known  at  the  moment  when  the  electrometer  deflection  is  being  recorded 
by  the  photographic  film. 

THEORETICAL  CONSIDERATIONS. 

Considerable  work  has  already  been  done,  notably  the  work  of 
Moseley,1  in  correlating  the  X-ray  spectra  of  the  different  elements  but 
little  progress  has  been  made  toward  determining  whether,  or  not,  the 
lines  of  a  single  element  might  be  grouped  into  series  such  as  some  of 
the  spectral  lines  in  ordinary  light  are  grouped  to  form  the  well-known 
Balmer's  series.  The  theoretical  work  of  Bohr2  shows  that  these  series 
in  the  case  of  some  of  the  lighter  elements  may  be  derived  from  a  theory 
of  atomic  structure  and  it  is  the  belief  of  many  that  X-rays  are  to  the 

1  Phil.  Mag.,  Vol.  26,  pp.  1024-34,  and  Vol.  27,  p.  703. 

2  Phil.  Mag.,  Vol.  26,  pp.  1-25,  pp.  476-505,  and  pp.  857-75. 


NoL6XL]  TUNGSTEN   X-RAY  SPECTRUM.  475 

heavier  elements  what  light  rays  are  to  those  of  lesser  atomic  weight. 
If  X-rays  are  produced  by  the  change  of  motion  of  electrons  near  the 
central  nucleus  it  might  be  possible  to  work  back  from  an  empirically 
derived  series  to  the  mechanism  by  which  these  rays  are  excited.  So  far 
such  a  series  has  not  been  found,  but  this  may  easily  be  due  to  the  fact 
that  so  far  only  a  comparatively  small  number  of  lines  has  been  found. 
The  failure  to  find  them  is  more  probably  due  to  a  lack  of  resolving  power 
rather  than  to  the  existence  of  but  few  lines.  In  the  case  of  the  plate 
giving  19  lines  in  the  L  group  the  resolving  power  was  less  than  170  and 
we  know  that  with  such  low  resolving  powers  we  would  have  learned 
but  little  of  that  which  we  now  know  of  light  spectra. 

By  the  use  of  Bohr's  theory  Kossel1  has  attempted  to  explain  the  origin 
of  the  K  and  L  radiations  by  assuming  several  stable  orbits  of  different 
radii  near  the  nucleus  and  that  the  hardest  of  the  K  lines  is  due  to  the 
falling  of  an  electron  from  the  outer  to  the  inner  orbit.  These  theories 
led  to  the  conclusion  that  the  difference  in  frequency  of  the  two  K  lines 
(at  the  time  he  wrote  the  K  lines  were  treated  as  only  two  but  these 
are  now  known  to  be  double  lines)  should  be  the  frequency  of  the  L 
line  of  longest  wave-length.  This  has  been  said  to  hold  true  for  a  number 
of  elements,  but  if  we  take  the  average  wave-length  of  the  K  doublets 
as  found  in  this  work  we  should  have 

ill 


.1809      .2100      XL* 

Whence  XL  =  1.30  instead  of  1.48  Angstrom  units  as  it  should  if  the 
theory  were  correct.  This  is  a  greater  variation  than  is  permissible, 
even  granting  the  greatest  possible  errors  in  these  measurements. 

SUMMARY. 

1.  This  work  shows  that  accurate  wave-length  measurements  and  the 
separation  of  close  doublets  can  only  be  achieved  by  limiting  the  thick- 
ness of  the  crystal  and  the  width  of  source  and  making  the  distance 
between  crystal  and  photographic  plate  as  great  as  is  practicable  with 
regard  to  the  necessary  intensity. 

2.  The  L  group  of  the  tungsten  X-ray  lines  by  these  means  is  shown 
to  contain  at  least  19  lines  and  measurements  correct  to  o.i  per  cent, 
are  given  of  their  wave-lengths.     From  considerations  of  the  resolving 
power  of  the  apparatus  it  seems  possible  that  the  true  number  may  be 
as  great  as  the  number  of  lines  in  the  light  spectra  of  an  element. 

3.  It  is  shown  that  the  K  lines  of  tungsten  may  be  clearly  separated 

1  Ber.  d.  Physik.  Gesel.,  Vol.  12,  p.  953,  1914. 


476  ELMER  DERSHEM. 

in  the  first  order  if  the  conditions  required  for  the  highest  practicable 
resolving  power  are  complied  with. 

In  conclusion  I  wish  to  thank  the  staff  of  the  physics  department  and 
especially  Professor  G.  W.  Stewart,  who  directed  the  work,  for  many 
helpful  suggestions  and  encouragement  in  the  carrying  out  of  this  task 
and  also  to  Mr.  A.  M.  McMahon,  who  gave  much  assistance  in  the 
performance  of  the  work. 

PHYSICS  LABORATORY, 
UNIVERSITY  OF  IOWA, 
December,  1917. 


BIOGRAPHY 

Elmer  Dershem  was  born  at  Norwood,  Kansas,  on  December 
31,  1881.  His  early  education  was  obtained  in  the  public  grade 
schools  of  Kansas  and  his  preparatory  education  in  the  Academy 
of  Baker  University  at  Baldwin,  Kansas.  He  entered  the  Uni- 
versity of  Kansas  in  1908  and  received  the  degree  of  B.  S.  in 
Electrical  Engineering  in  1912.  During  his  senior  year  he  was  also 
enrolled  as  a  graduate  student  in  mathematics.  He  was  employed 
for  two  years  in  the  Testing  Department  of  the  General  Electric 
Co.  at  Schenectady,  New  York,  and  also  at  Pittsfield,  Massa- 
chusetts. He  entered  the  State  University  of  Iowa  in  1914  as  a 
graduate  student  and  assistant  in  the  Department  of  Physics.  He 
was  granted  the  degree  of  M.  S.  in  Physics  in  1915,  the  title  of 
his  thesis  being  "Roentgen  Ray  Analysis  of  Crystal  Structure 
with  Special  Reference  to  Selenium  Crystals." 


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